What is 4x^2-4y^2+8x-4y-3=0 ?

The solution to 4x^2-4y^2+8x-4y-3=0 is Hyperbola with (h,k)=(-1,-1/2),a=sqrt(3/2),b=sqrt(3/2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4x^2-4y^2+8x-4y-3=0

4 x^{2} - 4 y^{2} + 8 x - 4 y - 3 = 0

(h, k) = (- 1, - \frac{1}{2}), a = \frac{3}{2}, b = \frac{3}{2}

Solution steps

4 x^{2} - 4 y^{2} + 8 x - 4 y - 3 = 0

Rewrite

4 x^{2} - 4 y^{2} + 8 x - 4 y - 3 = 0

in the form of a standard hyperbola equation

\frac{( x - ( - 1 ) ) ^{2}}{( \frac{3}{2} ) ^{2}} - \frac{( y - ( - \frac{1}{2} ) ) ^{2}}{( \frac{3}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 1, - \frac{1}{2}), a = \frac{3}{2}, b = \frac{3}{2}

y^{2} - 4 x^{2} - 12 y - 16 x \cdot 16 = 0

\frac{y ^{2}}{6} - 4 x^{2} = 1

y^{2} + 17 = 3 x^{2}

x^{2} - 2 x + 1 - y^{2} = 1

- x^{2} + y^{2} - 9 = 0

What is 4x^2-4y^2+8x-4y-3=0 ?
The solution to 4x^2-4y^2+8x-4y-3=0 is Hyperbola with (h,k)=(-1,-1/2),a=sqrt(3/2),b=sqrt(3/2)